Rate Optimisation

Fast approximate adjoint and forward simulation for finding optimal rates and/or well placements for water flooding optimization.

Basic Ideas

  • couple MsMFEM for pressure and a flow-based coarsening for saturation for fast forward and adjoint simulation
  • for additional speed-up, compute coarse-grid communication mappings in a preprocessing step prior to the optimization loop


Adjoint code developed for simulation of two-phase incompressible flow model on fine and coarse grids. Model speed-up through preprocessing applies both to forward and adjoint coarse models. For this simplified model, there is a natural relation between the adjoint variables on the fine and the coarse model through a dual coarse basis, which is similar, but not identical, to the forward coarse model basis. The methodology has been tested on rate-optimization for water flooding, and simple well-placement problems. Even coarse models with an upscaling factor of ~500 show good performance for optimization purposes.


  • enables fast approximate simulations without initial full model run / snapshots
  • incorporates geological/geometrical features even for high degree of coarsening
  • only well-bases need to be updated in well-placement optimization


Stein Krogstad, Vera Louise Hauge , Astrid Fossum Gulbransen. Adjoint multiscale mixed finite elements. SPE J., Vol. 16, No. 1, pp. 162-171, 2011. DOI: 10.2118/119112-PA.

Coarse pressure grid and coarse saturation grid


Initial fine-grid saturation (top left), initial coarse-grid saturation (bottom left). Optimized coarse saturation (bottom right) and the resulting finegrid saturation (top right).


Initial (left) and optimal (right) well placements. Producers in red, injecrtors in blue. 

Published October 21, 2010